Diatom-based total phosphorus (TP) and pH transfer functions for the Irish Ecoregion

A 72-lake diatom training set was developed for the Irish Ecoregion to examine the response of surface sediment diatom assemblages to measured environmental variables. A variety of multivariate data analyses was used to investigate environmental and biological data structure and their inter-relationships. Of the variables used in determining a typology for lakes in the Irish Ecoregion, alkalinity was the only one found to have a significant effect on diatom assemblages. A total of 602 diatom taxa were identified, with 233 recorded at three or more sites with abundances ≥1%. Generally diatom data displayed a high degree of heterogeneity at the species level and non-linear ecological responses. Both pH and total phosphorus (TP) (in the ranges of 5.1–8.5 and 4.0–142.3 μg l⁻¹ respectively) were shown to be the most significant variables in determining the surface sediment diatom assemblages. The calibration models for pH and TP were developed using the weighted averaging (WA) method; data manipulation showed strong influences on model performances. The optima WA models based on 70 lakes produced a jack-knifed coefficient of determination (r ² _jack) of 0.89 with a root mean squared error (RMSEP) of 0.32 for pH and r ² _jack of 0.74 and RMSEP of 0.21 (log₁₀ μg l⁻¹) for TP. Both models showed strong performances in comparison with existing models for Ireland and elsewhere. Application of the pH and TP transfer functions developed here will enable the generation of quantitative water quality data from the expanding number of palaeolimnological records available for the Irish Ecoregion, and thus facilitate the use of palaeolimnological approaches in the reconstruction of past lake water quality, ecological assessment and restoration.     

Diatom-based models for reconstructing past water quality and productivity in New Zealand lakes

The trophic status of lakes in New Zealand is, on average, low compared to more densely populated areas of the globe. Despite this, trends of eutrophication are currently widespread due to recent intensification in agriculture. In order to better identify baseline productivity and establish long-term trends in lake trophic status, diatom-based transfer functions for productivity-related parameters were developed. Water quality data and surface sediment diatom assemblages from 53 lakes across the North and South Islands of New Zealand were analysed to determine species responses to the principal environmental gradients in the data set. Repeat sampling of water chemistry over a 12-month period enabled examination of species responses to annual means as well as means calculated for stratified and mixed periods. Variables found to be most strongly correlated with diatom species distributions were chlorophyll a (Chl a), total phosphorus (TP), dissolved reactive phosphorus (DRP), ionic concentration (measured as electrical conductivity (EC)) and pH. These variables were used to develop diatom-based transfer functions using weighted averaging regression and calibration (simple, tolerance down-weighted and with partial least squares algorithm applied). Overall, models derived for stratified means were weaker than those using annual or isothermal means. For specific variables, the models derived for the isothermal mean of EC (WA-tol r²_jack = 0.79; RMSEP = 0.15 log₁₀ S cm^–1),the annual mean of pH (WA r²_jack = 0.72; RMSEP = 0.25 pH units) and the isothermal mean of Chl a (WA r²_jack = 0.71; RMSEP = 0.18 log₁₀ mg m^–3 Chl a) performed best. The models derived for TP were weak in comparison (for the annual mean of TP: WA r²_jack = 0.50; RMSEP = 0.24 log₁₀ mg m^–3 TP) and residuals on estimates for this model were correlated with several other water quality variables, suggesting confounding of species responses to TP concentrations. The model derived for the isothermal mean of DRP was relatively strong (WA-tol r²_jack = 0.78; RMSEP = 0.17 log₁₀ mg m^–3 DRP); however, residual values for this model were also found to be strongly correlated with several other water quality variables. It is concluded that the poor performance of the TP and DRP transfer functions relative to that of the Chl a model reflects the coexistence of nitrogen and phosphorus limitation within the lakes in the data set. In spite of this, the suite of transfer functions developed from the training set is regarded as a valuable addition to palaeolimnological studies in NewZealand.     

Diatom-based water chemistry reconstructions from northern Sweden: a comparison of reconstruction techniques

The diatom composition in surface sediments from 119 northern Swedish lakes was studied to examine the relationship with lake-water pH, alkalinity, and colour. Diatom-based predictive models, using weighted-averaging (WA) regression and calibration, partial least squares (PLS) regression and calibration, and weighted-averaging partial least squares (WA-PLS) regression and calibration, were developed for inferences of water chemistry conditions. The non-linear response between the diatom assemblages and pH and alkalinity was best modelled by weighted-averaging methods. The lowest prediction error for pH was obtained using weighted averaging, with or without tolerance downweighting. For alkalinity there was still some information in the residual structure after extracting the first weighted-averaging component, which resulted in a slight improvement of predictions when using a two component WA-PLS model. The best colour predictions were obtained using a two component PLS model. Principal component analysis (PCA) of the prediction errors, with some characteristics of the training set included as passive variables, was performed to compare the results for the different alkalinity predictive models. The results indicate that calibration techniques utilizing more than one component (PLS and WA-PLS) can improve the predictions for lakes with diatom taxa that have broad tolerances. Furthermore, we show that WA-PLS performs best compared with the other techniques for those lakes that have a high relative abundance of the most dominant taxa and a corresponding low sample heterogeneity.     

An expanded surface-water palaeotemperature inference model for use with fossil midges from eastern Canada

Using an expanded surface sample data set, representing lakes distributed across a transect from southernmost Canada to the Canadian High Arctic, a revised midge-palaeotemperature inference model was developed for eastern Canada. Modelling trials with weighted averaging (with classical and inverse deshrinking; with and without tolerance downweighting) and weighted averaging partial least squares (WA-PLS) regression, with and without square-root transformation of the species data, were used to identify the best model. Comparison of measured and predicted temperatures revealed that a 2 component WA-PLS model for square-root transformed percentage species data provided the model with the highest explained variance (r =0.88) and the lowest error estimate (RMSEP _jack =2.26 °C). Comparison of temperature inferences based on the new and old models indicates that the original model may have seriously under-estimated the magnitude of late-glacial temperature oscillations in Atlantic Canada. The new inferences suggest that summer surface water temperatures in Splan Pond, New Brunswick were approximately 10 to 12 °C immediately following deglaciation and during the Younger Dryas. During the Allerod and early Holocene, surface water temperatures of 20 to 24 °C were attained. The new model thus provides the basis for more accurate palaeotemperature reconstructions throughout easternmost Canada.     

Diatom-temperature transfer functions based on the altitudinal zonation of diatom assemblages in Papua New Guinea: a possible tool in the reconstruction of regional palaeoclimatic changes

Indirect and direct gradient ordination techniques were used to study the relationship between present-day benthic and periphytic diatom assemblages and environmental factors along an altitudinal gradient in Papua New Guinea. Both within the screened initial data-set and a narrowly-defined subset of soft-water lakes, shifts in diatom assemblages are clearly related to altitudinal differences. This relation is used to construct transfer functions for inferring altitude (and hence average water temperature) from the diatom records. Calibration by canonical correspondence analysis (CCA) and simple weighted averaging calibration proved to be superior to models using WA with tolerance downweighting and to a simple WA model based on a selection of 52 indicator taxa. From the calibration models and the linear relationship between altitude and epilimnetic water temperature, the average lake water temperature can be predicted with an accuracy of 3.2°C. After further refinement, a transfer function for palaeotemperature based on diatoms would be of potential value for climatic reconstructions in tropical regions.     

Sources of bias in weighted average inferences of environmental conditions

Weighted averaging is widely used for inferring environmental conditions from an observed species assemblage. However, weighted average inferences are known to be systematically biased, and linear corrections (i.e., deshrinking functions) are commonly applied to adjust for this bias. In this analysis, the magnitude of the biases in weighted average inferences (and therefore the values of the deshrinking coefficients) are shown to depend upon the range of conditions sampled in the calibration data set and the true optima and niche breadths of the species observed in the calibration data set. Since the range of conditions and the observed species can differ between the calibration data set and the new data set for which environmental conditions are inferred, the coefficients for the deshrinking function derived using the calibration data may not be applicable to inferences computed using a new data set. Thus, environmental inferences may still exhibit systematic errors even after application of the linear correction. The findings from the theoretical analysis are demonstrated using stream temperature and macroinvertebrate data collected from wadeable streams in the western United States.     

Cladoceran and chironomid assemblages as qualitative indicators of water depth in subarctic Fennoscandian lakes

The relationship between surface-sediment cladoceran and chironomid communities to lake depth was analysed in 53 lakes distributed across timberline in northern Fennoscandia using multivariate statistical approaches. The study sites are small and bathymerically simple, with water depth ranging from 0.85-27.0 m (mean 6.36 m). Maximum lake depth was the most important factor in explaining the cladoceran distributions and the second most important factor in explaining the chironomid distributions in these subarctic lakes, as assessed on the basis of a series of constrained RDAs, Monte Carlo permutation tests, and variance partitioning. Quantitative inference models for maximum lake depth were created for both groups of animals. Well-performing calibration functions for predicting lake depth were obtained in each case using linear partial least squares (PLS) regression and calibration, weighted averaging (WA) with an 'inverse' deshrinking regression, and weighted averaging partial least squares (WA-PLS). Quantitative reconstructions of lake level fluctuations should be possible from cladoceran and chironomid core data with a root mean squared error of prediction (RMSEP), as estimated by jack-knifing, of about 1.6-3.0 m.     

Maximum likelihood environmental calibration and the compute program WACALIB a correction

A recently discovered error in the part of the computer program WACALIB that implements maximum likelihood (ML) calibration has been discovered and corrected. The new version of WACALIB has been re-run with all the data-sets from which results based on the earlier version of WACALIB had been published. The new results suggest that ML regression and calibration perform as well or even better than weighted averaging (WA), at least when judged by the apparent root mean squared error. Further work involving cross-validation is required to evaluate more fully the relative performance of WA and ML approaches.     

Rescaling species optima estimated by weighted averaging

The common practice of linear deshrinking in weighted averaging is known to be equivalent to a linear rescaling of the estimated species optima. In published lists of species optima, the use of rescaling is recommended, as it allows values derived from different data sets to be compared and used for new inferences, assuming that taxonomic consistency is assured. Rescaling optima is also shown to influence WA estimates of species tolerances. Non-linear rescaling is also discussed, in the form of cubical rescaling and weighted averaging-partial least squares (WA-PLS). The use of a different deshrinking equation in a small data set did lead to similar prediction errors, probably because of the small size of the data set used.     

Diatom-based transfer functions for western Quebec lakes (Abitibiand Haute Mauricie): the possible role of epilimnetic CO2 concentration in influencing diatom assemblages

Surficial sediments from 76 lakes from two western Quebec regions(Abitibi and Haute Mauricie) were sampled to identify the relationships betweendiatoms and environmental variables. Because the two regions containedradically different diatom communities, we then investigated which factors maybe responsible for the large community discrepancies in the two nearbygeographical areas. Standard lake chemistry variables showed little differencesbetween the regions, although epilimnetic light regimes were slightly lower inAbitibi. Nevertheless, lakes of the two regions with similar light regimes andchemistry still showed a clear separation in their diatoms, implying that otherimportant factors are influencing assemblages. We found that the calculatedconcentration of CO₂ in the open water can explain some of thediscrepancy in diatom assemblages. A pCCA constrained to the concentration ofCO₂ with alkalinity and pH as covariables explained 12.5% of speciesvariance and was significant. Given the lack of a relationship between DOC andCO₂, and because the lakes are heavily supersaturated withCO₂ in the calibration set, lake-to-lake variations inCO₂ concentrations are likely due to groundwater inputs; thepossibility that this environmental variable may be influencing diatomcommunities might allow, in some cases, the reconstruction of historicalchanges in groundwater inputs to lakes. Finally, new calibration models werebuilt in Quebec by using weighted averaging partial least square(WA-PLS) techniques in order to infer pH, CO₂, TP, TN, and, DOC fromdiatom assemblages preserved in the surface sediments.     

A comparison between diatom-based pH inference models using Artificial Neural Networks (ANN), Weighted Averaging (WA) and Weighted Averaging Partial Least Squares (WA-PLS) regressions

We explored the possibility of using artificial neural networks (ANN) to develop quantitative inference models in paleolimnology. ANNs are dynamic computer systems able to learn the relations between input and output data. We developed ANN models to infer pH from fossil diatom assemblages using a calibration data set of 76 lakes in Quebec. We evaluated the predictive power of these models in comparison with the two most commonly methods used in paleolimnology: Weighted Averaging (WA) and Weighted Averaging Partial Least Squares (WA-PLS). Results show that the relationship between species assemblages and environmental variables of interest can be modelled by a 3-layer back-propagation network, with apparent R² and RMSE of 0.9 and 0.24 pH units, respectively. Leave-one-out cross-validation was used to access the reliabilities of the WA, WA-PLS and ANN models. Validation results show that the ANN model (R² _jackknife = 0.63, RMSE_jackknife = 0.45, mean bias = 0.14, maximum bias = 1.13) gives a better predictive power than the WA model (R² _jackknife = 0.56, RMSE_jackknife = 0.5, mean bias = –0.09, maximum bias = –1.07) or WA-PLS model (R² _jackknife = 0.58, RMSE_jackknife = 0.48, mean bias = –0.15, maximum bias = –1.08). We also evaluated whether the removal of certain taxa according to their tolerance changed the performance of the models. Overall, we found that the removal of taxa with high tolerances for pH improved the predictive power of WA-PLS models whereas the removal of low tolerance taxa lowered its performance. However, ANN models were generally much less affected by the removal of taxa of either low or high pH tolerance. Moreover, the best model was obtained by averaging the predictions of WA-PLS and ANN models. This implies that the two modelling approaches capture and extract complementary information from diatom assemblages. We suggest that future modelling efforts might achieve better results using analogous multi-model strategies.     

Assessing the performance of a diatom transfer function on four Minnesota lake sediment cores: effects of training set size and sample age

Paleolimnological information is often extracted from diatom records using weighted averaging calibration and regression techniques. Larger calibration sample sets yield better inferences because they better characterize the environmental characteristics and species assemblages of the sample region. To optimize inferred information from fossil assemblages, however, it is worth knowing if fewer calibration samples can be used. Furthermore, confidence in environmental reconstructions is greater if we consider the relative importance of (A) similarity between fossil and calibration assemblages and (B) how well fossil taxa respond to the environmental variable of interest. We examine these issues using ~200-year sediment profiles from four Minnesota lakes and a 145-lake surface sediment training set calibrated for total phosphorus (TP). Training set sample sizes ranging from 10 to 145 were created through random sample selection, and models based on these training sets were used to calculate diatom-inferred (DI) TP data from fossil samples. Relationships between DI-TP variability and sample size were used to determine the minimum sample size needed to optimize the model for paleo-reconstruction. Similarly, similarities between fossil and modern assemblages were calculated for each size training set. Finally, fossil and modern assemblages were compared to determine whether older fossil samples had poorer similarity with modern analogs. More than 50–80 samples, depending on lake, were needed to stabilize variability in DI-TP results, and >110 training set samples were needed to minimize modern-fossil assemblage dissimilarities. Dissimilarities appeared to increase with sample age, but only one of the four studied cores displayed a significant trend. We have two recommendations for future studies: (1) be cautious when dealing with smaller training sets, especially if they are used to interpret older fossil assemblages and (2) understand how well fossil taxa are attuned to the variable of interest, as it is critical to evaluating the quality of the diatom-inferred data.     

Scaled chrysophytes and pH inference models: the effects of converting scale counts to cell counts and other species data transformations

Predictive pH models developed using scaled chrysophytes (Synurophyceae, Chrysophyceae) have thus far been based on the relative abundance of scales and not whole cells. This paper examines the effects of transforming scale to cell numbers on the predictive abilities of pH inference models, and the effects of logarithmic and square-root transformations of the species data on the predictive abilities of pH inference models.Very similar pH inference models were developed based on either the relative abundance of scales or cells. Thus, in this data-set, there appears to be no statistical advantage in transforming raw scale counts to cell counts prior to calculating the relative abundances. However, if one wishes to compare paleochrysophyte populations to actual long-term limnological chrysophyte collections, a scale-to-cell transformation would be desirable. Logarithmic and square-root transformations of the species data improve the pH inference models. These transformations increase the effective number of occurrences of chrysophyte taxa when compared to the untransformed scale and cell pH models. The logarithmic and square-root transformations improve the pH inference models because the dominant taxa, which are often pH generalists, are down-weighted in comparison to the more pH specialist, sub-dominant taxa. We suggest researchers use either a logarithmic or square-root transformation on chrysophyte scale data to improve quantitative reconstructions of lakewater pH and possibly other variables.     

A diatom model for inferring sea level change in the coastal waters of Hong Kong

Diatoms were identified and enumerated from surface sediments of 25 sites in Double Haven, Hong Kong. The relationship between diatom species distribution and 14 environmental variables was examined using Detrended Correspondence Analysis (DCA) and Canonical Correspondence Analysis (CCA). Water depth was identified as the most important environmental variable influencing the distribution of diatoms in Double Haven. Subsequently a Weighted Average (WA) calibration model was developed to infer water depth. The reliability of the model was evaluated by the error of prediction (RMSE_boot= 3.479) and the correlation (r ²= 0.7342) between observed and diatom-inferred values. This predictive calibration model has the potential to infer past sea level change in Hong Kong and the adjacent coastal areas.     

Estimation of pH optima and tolerances of diatoms in lake sediments by the methods of weighted averaging,least squares and maximum likelihood,and their use for the prediction of lake acidity

Ecological optima and tolerances with respect to autumn pH were estimated for 63 diatom taxa in 47 Finnish lakes. The methods used were weighted averaging (WA), least squares (LS) and maximum likelihood (ML), the two latter methods assuming the Gaussian response model.WA produces optimum estimates which are necessarily within the observed lake pH range, whereas there is no such restriction in ML and LS. When the most extreme estimates of ML and LS were excluded, a reasonably close agreement among the results of different estimation methods was observed. When the species with unrealistic optima were excluded, the tolerance estimates were also rather similar, although the ML estimates were systematically greater.The parameter estimates were used to predict the autumn pH of 34 other lakes by weighted averaging. The ML and LS estimates including the extreme optima produced inferior predictions. A good prediction was obtained, however, when prediction with these estimates was additionally scaled with inverse squared tolerances, or when the extreme values were removed (censored). Tolerance downweighting was perhaps more efficient, and when it was used, no additional improvement was gained by censoring. The WA estimates produced good predictions without any manipulations, but these predictions tended to be biased towards the centroid of the observed range of pH values.At best, the average bias in prediction, as measured by mean difference between predicted and observed pH, was 0.082 pH units and the standard deviation of the differences, measuring the average random prediction error, was 0.256 pH units.     

WACALIB version 3.3 — a computer program to reconstruct environmental variables from fossil assemblages by weighted averaging and to derive sample-specific errors of prediction

A computer program for reconstructing environmental variables (e.g. lake-water pH) from fossil assemblages (e.g. diatoms) by weighted averaging regression and calibration is described. The estimation of sample-specific errors of prediction by bootstrapping is outlined. The program runs on IBM-compatible personal computers.     

‘Diatoms and pH reconstruction’ (1990) revisited

The 167 sample lake-water pH-diatom calibration data-set created as part of the Palaeolimnology Programme within the Surface Water Acidification Project (SWAP) is re-analysed numerically using nine different numerical methods, six based on simple two-way weighted-averaging (WA), and the other three involving Gaussian logit regression (GLR) and maximum-likelihood (ML) calibration, the modern analogue technique, or weighted-averaging partial least-squares regression and calibration. Root mean squared error of prediction and maximum bias were estimated for all nine methods based on 10,000 internal and 10,000 external cross-validations involving a training-set, an optimisation-set, and a test-set. The results show that WA with a monotonic deshrinking spline equals or slightly outperforms WA with linear inverse deshrinking, especially in external cross-validation. Methods that employ tolerance downweighting generally have an inferior performance except when combined with monotonic deshrinking. It appears that simple two-way WA extensively used in SWAP cannot be significantly bettered. Thanks to increased computing power, better software, and more rigorous cross-validations, GLR shows good performance, especially in external cross-validation.     

An ostracod-conductivity transfer function for Tibetan lakes

About 145 freshwater to hypersaline lakes of the eastern Tibetan Plateau were investigated to develop a transfer function for quantitative palaeoenvironmental reconstructions using ostracods. A total of 100 lakes provided sufficient numbers of ostracod shells. Multivariate statistical techniques were used to analyse the influence of a number of environmental variables on the distributions of surface sediment ostracod assemblages. Of 23 variables determined for each site, 19 were included in the statistical analysis. Lake water electrical conductivity (8.2%), Ca% (7.6%) and Fe% (4.8%, ion concentrations as % of the cations) explained the greatest amounts of variation in the distribution of ostracod taxa among the 100 lakes. Electrical conductivity optima and tolerances were calculated for abundant taxa. A transfer function, based on weighted averaging partial least squares regression (WA-PLS), was developed for electrical conductivity (r ² = 0.71, root-mean-square-error of prediction [RMSEP] = 0.35 [12.4% of gradient length], maximum bias = 0.64 [22.4% of gradient length], as assessed by leave-one-out cross-validation) based on 96 lakes. Our results show that ostracods provide reliable estimates of electrical conductivity and can be used for quantitative palaeoenvironmental reconstructions similarly to more commonly used diatom, chironomid or pollen data.     

Reconstructing epilimnetic total phosphorus using diatoms: statistical and ecological constraints

Diatoms respond rapidly to eutrophication and diatom-based models for inferring total phosphorus (TP) have found wide application in palaeolimnology, especially in tracking trajectories of past and recent nutrient enrichment and in establishing pre-disturbance targets for restoration. Using new analysis of existing training sets and sediment-cores we examine the statistical and ecological constraints of diatom-inferred TP (DI-TP) models. Although the models show an apparently strong relationship between measured and inferred TP in the training sets, even under cross-validation, the models display three fundamental weaknesses, namely (1) the relationship between TP and diatom relative abundance is heavily confounded with secondary variables such as alkalinity and lake depth, (2) the models contain many taxa that are not significantly related to TP, and (3) comparison between different models shows poor or no spatial replicability. At some sites the sediment-core diatom assemblage change tracks the TP gradient in the training sets and DI-TP reconstructions are consistent with monitored TP data and known catchment histories for the recent past. At others diatom species turnover is apparently related to variables other than TP, and DI-TP fails to even reproduce plausible trends. Pre-disturbance DI-TP values are also questionable at most sites. We argue that these problems pervade many DI-TP models, particularly those where violations of the basic assumptions of the transfer function approach are ignored.